Modeling capillary hysteresis in unsatured porous media
Gérard Gagneux, Olivier Millet · Mathematics and Mechanics of Complex Systems · 2016
This paper deals with the modeling of cyclic hysteresis phenomena for flows in unsaturated porous media, using a dynamic regularization process of Sobolev type.The addition of a kinematic regularizing term of third-order partial derivatives, depending on a strictly positive, small real parameter, enables us to capture the missing information of the ill-posed hysteresis phenomena via Rankine-Hugoniot and "entropy" inequalities.When this parameter tends to zero, an oriented hysteresis loop, corresponding to the realistic problem modeled, emerges from the flow of an associated auxiliary ordinary differential equation.